Aircraft fan with low part-span solidity

ABSTRACT

A fan for a gas turbine engine includes: an annular casing; a disk disposed inside the casing and mounted for rotation about an axial centerline, the disk including a row of fan blades extending radially outwardly therefrom; each of the fan blades including an airfoil having circumferentially opposite pressure and suction sides extending radially in span from a root to a tip, and extending axially in chord between spaced-apart leading and trailing edges, with the airfoils defining corresponding flow passages therebetween for pressurizing air; the row including no more than 21 and no less than 13 of the fan blades; and wherein each of the fan blades has a solidity defined by a ratio of the airfoil chord over a circumferential pitch of the fan blades, measured at 60% of a radial distance from the root to the tip, of less than about 1.6.

BACKGROUND OF THE INVENTION

The present invention relates generally to aircraft engines, and morespecifically to aircraft engines incorporating a fan.

In a turbofan engine air is pressurized in a compressor and mixed withfuel in a combustor for generating hot combustion gases. A high pressureturbine (HPT) extracts energy from the combustion gases to power thecompressor. A low pressure turbine (LPT) extracts additional energy fromthe combustion gases to power the fan disposed upstream from thecompressor.

The primary design objective of aircraft turbofan engines is to maximizeefficiency thereof for propelling an aircraft in flight, andcorrespondingly reduce fuel consumption. Accordingly, the various coldand hot section rotor and stator components which define the internalflow passages for the pressurized air and combustion gases, and whichextract energy from those gases, are specifically designed formaximizing the efficiency thereof while correspondingly obtaining a longuseful life.

The turbofan itself includes a row of large fan rotor blades extendingradially outwardly from the perimeter of a supporting rotor disk. Thefan is powered by the LPT for pressurizing the incident air forproducing a majority of propulsion thrust discharged from the fanoutlet. Some of the fan air is channeled into the compressor wherein itis pressurized and mixed with fuel for generating the hot combustiongases from which energy is extracted in the various turbine stages, andthen discharged through a separate core engine outlet.

Turbofan engines are continually being developed and improved formaximizing their thrust capability with the greatest aerodynamicefficiency possible. Since the fan produces a substantial amount ofthrust during operation, noise is also generated therefrom and should bereduced as much as possible consistent with the various competing designobjectives.

For example, fan blades are typically designed for maximizing theaerodynamic loading thereof to correspondingly maximize the amount ofpropulsion thrust generated during operation. However, fan loading islimited by stall, flutter, or other instability parameters of the airbeing pressurized.

Accordingly, modem turbofan engines are designed with a suitable valueof stability and stall margin over their operating cycle from takeoff tocruise to landing of the aircraft to ensure acceptable operation andperformance of the engine without overloading the capability of theturbofan.

Furthermore, modem turbofan engines have relatively large diameterturbofans which rotate at sufficient rotary velocity to createsupersonic velocity of the blade tips relative to the incident airstream. The blade tips are therefore subject to the generation of shockwaves as the air is channeled and pressurized in the corresponding flowpassages defined between adjacent fan blades.

Accordingly, each fan blade is specifically tailored and designed fromits radially inner platform to its radially outer tip and along itscircumferentially opposite pressure and suction sides which extend inchord axially between the opposite leading and trailing edges thereof.The pressure side of one airfoil defines with the suction side of anadjacent airfoil the corresponding flow passage from root to tip of theblades through which the air is channeled during operation.

Each airfoil is typically twisted with a corresponding angle of staggerfrom root to tip, with airfoil tips being aligned obliquely between theaxial and circumferential directions of the fan.

During operation, the incoming ambient air flows at different relativevelocities through the inter-blade flow passages from root to tip of theblades including subsonic airflow at the blade roots and radiallyoutwardly thereof up to the supersonic velocity of the air at the bladetips in various portions of the operating range.

Fan stall margin is a fundamental design requirement for the turbofanand is affected by the aerodynamic fan loading, the fan solidity, andthe fan blade aspect ratio. These are conventional parameters, with thefan loading being the rise in specific enthalpy across the fan bladesdivided by the square of the tip speed.

Blade solidity is the ratio of the blade chord, represented by itslength, over the blade pitch, which is the circumferential spacing ofthe blades at a given radius or diameter from the axial centerline axis.In other words, blade pitch is the circumferential length at a givendiameter divided by the number of blades in the full fan blade row. And,the fan blade aspect ratio is the radial height or span of the airfoilportion of the blade divided by its maximum chord.

Conventional experience or teachings in the art indicate that when inletMach numbers are sufficiently high that passage shock can separate thesuction surface boundary layer of the air in the inter-blade flowpassages, good efficiency requires that the solidity should be high toallow the flow to reattach.

Conventional design practice for turbofan efficiency and adequate fanstall margin typically require the relatively high tip solidity which isgenerally equal to the fan tip relative Mach number at the design point,such as cruise operation. In other words, the tip Mach number issuitably greater than one (1.0) for supersonic flow, and the fan tipsolidity is correspondingly greater than one and generally equal to thetip relative Mach number for good designs.

The design considerations disclosed above are merely some of the manycompeting design parameters in designing a modem turbofan primarily forgood aerodynamic performance and efficiency, as well as for goodmechanical strength for ensuring a long useful life thereof. Each fanblade twists from root to tip, and the opposite pressure and suctionsides thereof also vary in configuration to specifically tailor the flowpassages from root to tip for maximizing fan efficiency with suitablestall margin and mechanical strength.

The resulting turbofan design is a highly complex design with threedimensional variation of the pressure and suction sides of theindividual airfoils across their axial chord and over their radial span.And, the individual fan blades cooperate with each other in the full rowof blades to define the inter-blade flow passages and to effect theresulting aerodynamic performance and stall margin of the entire fan.

Accordingly, it is desired to further improve the efficiency of themodern turbofan while maintaining adequate stability and stall marginnotwithstanding the various competing design objectives addressed inpart above.

BRIEF DESCRIPTION OF THE INVENTION

According to one aspect of the technology described herein, a fan forpowering an aircraft in flight includes: an annular casing; a diskdisposed inside the casing and mounted for rotation about an axialcenterline, the disk including a row of fan blades extending radiallyoutwardly therefrom; each of the fan blades including an airfoil havingcircumferentially opposite pressure and suction sides extending radiallyin span from a root to a tip, and extending axially in chord betweenspaced-apart leading and trailing edges, with the airfoils definingcorresponding flow passages therebetween for pressurizing air; the rowincluding no more than 21 and no less than 13 of the fan blades; andwherein each of the fan blades has a solidity defined by a ratio of theairfoil chord over a circumferential pitch of the fan blades, measuredat 60% of a radial distance from the axial centerline to the tip, ofless than about 1.6.

According to another aspect of the technology described herein, a methodis provided of operating a fan of the type including a disposed insidean annular casing, the disk rotatable about an axial centerline andcarrying a row of fan blades, wherein each of the fan blades includes anairfoil having spaced-apart pressure and suction sides extendingradially in span from a root to a tip, and extending axially in chordbetween spaced-apart leading and trailing edges, the row including nomore than 21 and no less than 13 of the fan blades, wherein each of thefan blades has a solidity defined by a ratio of the airfoil chord to acircumferential pitch of the fan blades, measured at 90% of a distancefrom the axial centerline to the tip, of no greater than about 1.2 andno less than about 1.0. The method includes: powering the fan in aturbofan engine to propel an aircraft in flight, such that a relativeMach number at the tips of the fan blades is greater than 1.0, and suchthat a ratio of the solidity measured at 90% of the distance from theaxial centerline to the tips to the relative Mach number at the sameradial location, is less than about 0.90.

According to another aspect of the technology described herein, a methodis provided of designing a fan of the type including a disposed insidean annular casing, the disk rotatable about an axial centerline andcarrying a row of fan blades, wherein each of the fan blades includes anairfoil having spaced-apart pressure and suction sides extendingradially in span from a root to a tip, and extending axially in chordbetween spaced-apart leading and trailing edges, the row including nomore than 21 and no less than 13 of the fan blades, wherein each of thefan blades has a solidity defined by the ratio of the airfoil chord to acircumferential pitch of the fan blades. The method includes:establishing a predetermined relative Mach number at the tips of the fanblades which is no less than about 1.0; selecting a chord of the fanblades, given the predetermined relative Mach number, such that a ratioof the solidity, measured at 90% of the distance from the axialcenterline to the tips to the relative Mach number at the same radiallocation, is less than about 0.90.

According to another aspect of the technology described herein, anaircraft engine for powering an aircraft in flight includes: a fan,including: an annular casing; a disk disposed inside the casing andmounted for rotation about an axial centerline, the disk including a rowof fan blades extending radially outwardly therefrom; each of the fanblades including an airfoil having circumferentially opposite pressureand suction sides extending radially in span from a root to a tip, andextending axially in chord between spaced-apart leading and trailingedges, with the airfoils defining corresponding flow passagestherebetween for pressurizing air; the row including no more than 21 andno less than 13 of the fan blades; and wherein each of the fan bladeshas a solidity defined by a ratio of the airfoil chord over acircumferential pitch of the fan blades, measured at 60% of a radialdistance from the axial centerline to the tip, of less than about 1.6;and a prime mover coupled to the fan and operable to drive the fan inflight.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention, in accordance with preferred and exemplary embodiments,together with further objects and advantages thereof, is moreparticularly described in the following detailed description taken inconjunction with the accompanying drawings in which:

FIG. 1 is a partly schematic isometric view of a turbofan in an aircraftengine for powering an aircraft in flight;

FIG. 2 is an axial sectional view through the turbofan portion of theengine illustrated in FIG. 1 and taken along line 2-2;

FIG. 3 is a forward-facing-aft elevational view of the turbofanillustrated in FIG. 1 and taken along line 3-3;

FIG. 4 is a top planform view of two adjacent fan blades illustrated inFIG. 3 and taken generally along line 4-4;

FIG. 5 is a graph showing blade solidity plotted against percent radiusfor an exemplary fan; and

FIG. 6 is a graph showing a ratio of blade solidity to relative Machnumber plotted against percent radius.

DETAILED DESCRIPTION OF THE INVENTION

Illustrated in FIG. 1 is an aircraft engine 10 configured for poweringan aircraft 12 in flight, and suitably mounted therein. The engine isaxisymmetrical about a longitudinal or axial centerline axis andincludes a fan or turbofan 14 suitably mounted coaxially inside asurrounding annular fan casing 16.

During operation, ambient air 18 enters the inlet end of the fan 14 andis pressurized thereby for producing thrust for propelling the aircraftin flight. The fan 14 is drive by a prime mover 15 which is illustratedschematically by a dashed line in FIG. 1. The prime mover may be anydevice operable to rotate the fan 14 at the required speed underexpected mechanical and aerodynamic loads. Nonlimiting examples of primemovers include heat engines, motors (e.g. electric, hydraulic, orpneumatic), or combinations thereof (for example electric hybrid). Thefan 14 may be driven directly by the prime mover 15, or through anintermediate geartrain. In the illustrated example, the prime mover 15comprises a gas turbine engine. A portion of the fan air is suitablychanneled in turn through a low pressure or booster compressor 20 and ahigh pressure compressor 22 which further pressurize the air in turn.

The pressurized air is mixed with fuel in an annular combustor 24 forgenerating hot combustion gases 26 which are discharged in thedownstream direction. A high pressure turbine (HPT) 28 first receivesthe hot gases from the combustor for extracting energy therefrom, and isfollowed in turn by a low pressure turbine (LPT) 30 which extractsadditional energy from the combustion gases discharged from the HPT. TheHPT is joined by one shaft or rotor to the high pressure compressor 22,and the LPT is joined by another shaft or rotor to both the boostercompressor 20 and the fan 14 for powering thereof during operation.

The exemplary turbofan engine 10 illustrated in FIG. 1 may have anyconventional configuration and operation for powering an aircraft inflight from takeoff to cruise to landing, but is modified as furtherdescribed hereinbelow for increasing the aerodynamic efficiency of thefan 14 while maintaining suitable stability and stall margin thereofduring the operating cycle.

More specifically, FIGS. 1 and 2 illustrate an exemplary embodiment ofthe turbofan 14 which includes a row of fan rotor blades 32 extendingradially outwardly in span from the perimeter rim of a supporting rotordisk 34. As shown in FIG. 2, each blade includes an airfoil 36 extendingoutwardly from a platform 38 defining the radially inner boundary of thefan air flowpath, which platform may be integrally formed with theairfoil or a separate component. The principles of the present inventionapply equally to a fan having a disk with separate blades as well as toa fan having the blades integrally formed with the disk, often referredto as a “bladed disk”, “integrally-bladed rotor”, or “blisk”. In thespecific example illustrated, each blade also includes an integraldovetail 40 extending radially inwardly from the airfoil below theplatform for mounting each blade in a corresponding dovetail slot in therim of the rotor disk 34.

The fan blades 32 may be made from suitable high strength materials liketitanium or carbon fiber composites. For example, the majority of thefan blade 32 may be formed of carbon fiber composite reinforced withtitanium shields along the leading and trailing edges, and along thetip.

As illustrated in FIGS. 1 and 2, each airfoil 36 has a suitableaerodynamic configuration including a generally concave pressure side 42and a circumferentially opposite, generally convex suction side 44. Theopposite sides of each airfoil extend radially in span from the innerroot end thereof at the platform 38 to the radially outer distal tip 46disposed closely adjacent to the fan stator casing 16 for providing arelatively small tip clearance or gap therebetween.

As shown in FIGS. 2 and 3, each airfoil extends axially in chord Cbetween opposite leading and trailing edges 48, 50, with the chordvarying in length over the span of the airfoil.

As shown in FIG. 4, adjacent airfoils 36 define circumferentiallytherebetween corresponding flow passages 52 for pressurizing the air 18during operation. Each of the airfoils 36 may include stagger or twistrepresented by the stagger angle A from the axial or longitudinal axis,which stagger increases between the root and tip of the airfoil.

For example, the stagger angle A at the blade tip 46 may be substantial,and about 60 degrees, to position the leading edge 48 of one airfoilcircumferentially adjacent but axially spaced from the suction side 44of the next adjacent airfoil aft from the leading edge thereof to definea corresponding mouth 54 for the flow passage between the opposingpressure and suction sides of the adjacent airfoils. The contours andstagger of the adjacent airfoils over the radial span of the bladescause each flow passage to converge or decrease in flow area to a throat56 of minimum flow area spaced aft from the mouth along most, if notall, of the radial span.

As further illustrated in FIG. 4, the relatively high airfoil stagger Aalso positions the trailing edge 50 of one airfoil 36 circumferentiallyadjacent to the pressure side 42 of the next adjacent airfoil while alsobeing spaced axially therefrom in the tip region to define acorresponding discharge or outlet 58 for the corresponding flow passagebetween adjacent airfoils. In this way, the incoming air 18 is channeledin the corresponding flow passages 52 between adjacent airfoils as theyrotate clockwise in FIGS. 1, 3, and 4 for pressurizing the air toproduce the propulsive thrust during operation.

FIGS. 1 and 2 also illustrate that the turbofan includes an annular tipshroud 62 suitably mounted flush inside the fan stator casing 16 anddirectly surrounding the airfoil tips 46 which are positioned closelyadjacent thereto to define a correspondingly small tip clearancetherewith. The tip shroud 62 may be conventional in configuration, suchas a lightweight honeycomb structure, with a substantially smooth innersurface facing the blade tips. The low solidity turbofan enjoys improvedefficiency while maintaining adequate stability and stall margin withoutthe need for stability enhancing features such as annular grooves whichcould otherwise be formed in the tip shroud.

As shown in FIG. 2, the fan casing 16 is spaced radially outwardly froman inner casing 64 which surrounds the core engine to define an annularbypass duct 66 radially therebetween. The aft end of the bypass duct 66defines the outlet for a majority of the fan air used in producingpropulsive thrust for the engine.

Spaced downstream or aft from the row of fan blades 32 is a row ofoutlet guide vanes 68 extending radially inwardly from the fan casing 16to join the inner casing 64.

As seen in FIG. 3, the fan blades 32 are of suitably large outerdiameter D for effecting supersonic airflow at the tips duringoperation. The fan 14 also has a corresponding solidity which is aconventional parameter equal to the ratio of the airfoil chord C, asrepresented by its length, divided by the circumferential pitch P orspacing from blade to blade at the corresponding span position orradius.

The circumferential pitch is equal to the circumferential length at thespecific radial span divided by the total number of fan blades in theblade row. Accordingly, the solidity is directly proportional to thenumber of blades and chord length and inversely proportional to thediameter.

Conventional practice as indicated above requires relatively highsolidity for maintaining good efficiency in a supersonic blade designsubject to shock in the flow passages between the adjacent airfoils.

However, it has been discovered that notwithstanding this conventionalpractice for relatively high solidity in modern turbofans, a substantialimprovement in efficiency while maintaining adequate stability and stallmargin may be obtained by decreasing solidity, and not increasingsolidity. As indicated above, solidity is proportional to the number offan blades and the ratio of the airfoil chord divided by the diameter ofthe fan.

Accordingly, solidity may be decreased by decreasing the number of fanblades, decreasing the airfoil chord, or increasing the outer diameterof the fan. However, the fan outer diameter is typically a givenparameter for a specifically sized turbofan engine.

It is further noted that fan blades for a particular fan would tend tohave approximately the same thickness dimension even if the chorddimension is varied, because the thickness dimension is usually set forstructural reasons as opposed to aerodynamic reasons. Accordingly, aparameter referred to as “thickness blockage” tends to be less when theblade count is lower. For this reason, considering a given solidity,there is an efficiency advantage to achieving this solidity in partthrough a lower blade count.

Accordingly, aerodynamic efficiency may be improved in a turbofan engine10 by using a relatively smaller number of fan blades 32 is compared toprior art designs. In one, the fan 14 may include thirteen to twenty-onefan blades 32. In another example, the fan 14 may include fifteen totwenty fan blades 32.

The reduction in number of fan blades increases the circumferentialpitch P between the airfoils and increases the flow area of the flowpassages 52, in particular at the throats 56 thereof, for reducing flowblockage during operation. The tip solidity of the turbofan 14 isrelatively low in magnitude, while still being greater than about 1.0 toprovide a circumferential gap G between the leading and trailing edges48, 50 of adjacent tips 46.

The airfoil tips 46 are locally angled and vary in width between theleading and trailing edges 48, 50 to typically converge the flow passage52 at the airfoil tips from the mouth 54 to the throat 56 and thendiverge the flow passage also at the tip from the throat 56 to theoutlet 58. Alternatively, the mouth and throat of the flow passages atthe airfoil tips may be coincident in one plane at the leading edges,with the flow passages still diverging aft from the throats at theleading edges to the passage outlets at the trailing edges.

The turbofan design may itself be otherwise conventional except asspecifically described herein For example, the airfoils 36 illustratedin FIGS. 1-4 are relatively large in diameter for supersonic tipoperation in a modem turbofan engine. The corresponding bypass ratio ofthe fan air which bypasses the core engine may be about 7.5 or greater.

The airfoils may be provided with suitable aerodynamic sweep which ispreferably forward or negative (S−) at the tips 46 of the airfoils, andpreferably negative along both the leading and trailing edges 48, 50thereof. The individual airfoils may have a large chord barreling neartheir midspan as illustrated in FIG. 2 with aft or positive aerodynamicsweep (S+) along a portion of the leading edge above the midspan ifdesired. The forward tip sweep in the fan blades improves efficiencyduring supersonic operation of the blade tips.

It has been found that reduction of solidity at locations inboard of thetip 46 is useful to improve aerodynamic performance and/or aerodynamicefficiency of the fan 14. This reduction of solidity may be implementedby reducing chord C at locations inboard of the tip 46.

FIG. 5 illustrates the characteristics of the fan design according to anaspect of the present invention (shown by a line with triangularmarkers) as compared to a prior art design (shown by a line with squaremarkers). It can be seen that, while the solidity is close to 1.0 at thetip for both designs, the solidity of the fan 14 is lower at alllocations inboard of the tip. The offset graph describing the loweredsolidity at inboard locations may be characterized by the solidityvalues at representative locations along the span.

One representative location is at 90% of the radial distance from theaxial centerline to the tip, also referred to herein as “90% of tipradius”. For example, the fan 14 may have a solidity measured at 90% oftip radius, of about 1.0 to about 1.2. As used herein, the term “about”encompasses the stated value or range of values, as well as variationsor deviations from the stated value or range of values that do notsignificantly affect aerodynamic behavior compared to the stated valueor range of values, and/or are caused by errors in measurement, and/orare caused by variation in manufacturing processes.

Another representative location is at 60% of the radial distance fromthe axial centerline to the tip, also referred to herein as “60% of tipradius”. For example, the fan 14 may have a solidity measured at 60% oftip radius, of less than about 1.6. As another example, the fan 14 mayhave a solidity, measured at 60% of tip radius, of no greater than about1.4.

Another representative location is at 30% of the radial distance fromthe axial centerline to the tip, also referred to herein as “30% of tipradius”. For example, the fan 14 may have a solidity, measured at 30% ofthe radial distance from the root to the tip, of less than about 2.2. Asanother example, the fan 14 may have a solidity, measured at 30% of tipradius, of no greater than about 1.9.

It has been further found that consideration of the ratio of solidity torelative Mach number (abbreviated “M_(rel)”) at locations inboard of thetip is also useful in improving efficiency. It will be understood thatthe relative Mach number will vary during operation of the engine 10depending on the phase of operation (e.g. idle, take-off, climb, cruise,approach, landing) as well as prevailing atmospheric conditions. Whenthe term Mach number or relative Mach number is discussed herein, itwill be understood that this refers to a value that is selected to besignificant for design purposes. For example, the Mach number consideredfor design purposes may be a value representative of the expected Machnumber at level cruise flight conditions. As used herein, “level cruiseflight” refers to extended operation at a stabilized altitude and Machnumber.

FIG. 6 illustrates the characteristics of the fan design according to anaspect of the present invention (shown in a dashed line) as compared toa prior art design (shown in a solid line). It can be seen that, whileratio of solidity to relative Mach number is close to 1.0 at the tip forboth designs, the ratio of the fan 14 is lower at all locations inboardof the tip. The offset graph describing the lowered ratio at inboardlocations may be characterized by the solidity/M_(rel) values atrepresentative locations along the span.

One representative location is at 90% of tip radius. For example, givena predetermined relative Mach number, the solidity may be selected suchthat the ratio solidity/M_(rel) is less than about 0.90. As anotherexample, the solidity of the may be set, given a predetermined relativeMach number, such that the ratio solidity/Mrel is no greater than about0.87.

Another representative location is at 60% of tip radius. For example,given a predetermined relative Mach number Mrel, the fan 14 may have aratio solidity/M_(rel), measured at 60% of tip radius, of less thanabout 1.50. As another example, the fan 14 may have a ratiosolidity/M_(rel), measured at 60% of tip radius, of about 1.35 or less.

Another representative location is at 30% of tip radius. For example,given a predetermined relative Mach number Mrel, the fan 14 may have aratio solidity/M_(rel), measured at 30% radius, of less than about 3.20.As another example, the fan 14 may have a ratio solidity/M_(rel),measured at 30% of tip radius, of about 2.81 or less.

Any of the fans 14 described above may be designed in part byestablishing a predetermined relative Mach number at a specific radiallocation, and then given that predetermined relative Mach number,selecting a chord of the fan blades 32 at the specific radial location,to result in the desired ratio of the solidity to the relative Machnumber.

The fan 14 may be used by powering the fan 14 in the turbofan engine 10to propel an aircraft (not shown) in atmospheric flight, such that arelative Mach number at the tips of the fan blades is greater than 1.0.

The low solidity turbofan disclosed above may be used in various designsof modern turbofan aircraft gas turbine engines for improving efficiencythereof. Particular advantage is obtained for relatively large diametertransonic turbofans in which the blade tips are operated with supersonicairflow.

Analysis of the fans disclosed above has confirmed an increase inaerodynamic efficiency thereof as compared to prior art fans, whilemaintaining adequate stability and stall margin. The reduced blade countcorrespondingly reduces engine weight and cost.

While there have been described herein what are considered to bepreferred and exemplary embodiments of the present invention, othermodifications of the invention shall be apparent to those skilled in theart from the teachings herein, and it is, therefore, desired to besecured in the appended claims all such modifications as fall within thetrue spirit and scope of the invention.

What is claimed is:
 1. A method of operating a fan of the type including a disk disposed inside an annular casing, the disk rotatable about an axial centerline and carrying a row of fan blades, wherein each of the fan blades includes an airfoil having spaced-apart pressure and suction sides extending radially in span from a root to a tip, and extending axially in chord between spaced-apart leading and trailing edges, the row including no more than 21 and no less than 13 of the fan blades, wherein each of the fan blades has a solidity defined by a ratio of the airfoil chord to a circumferential pitch of the fan blades, measured at 90% of a radial distance from the axial centerline, to the tip, of no greater than about 1.2 and no less than about 1.0, the method comprising: powering the fan to propel an aircraft in level cruise flight, such that a relative Mach number at the tips of the fan blades is greater than 1.0, and such that a ratio of the solidity measured at 90% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is less than about 0.90.
 2. The method of claim 1 wherein a ratio of the solidity measured at 90% of a radial distance from the axial centerline, to the relative Mach number at the same radial location is no greater than about 0.87.
 3. The method of claim 2 wherein: a ratio of the solidity measured at 60% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 1.35.
 4. The method of claim 1 wherein: a ratio of the solidity measured at 60% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 1.50.
 5. The method of claim 4 wherein: a ratio of the solidity measured at 30% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 3.20.
 6. The method of claim 5 wherein: a ratio of the solidity measured at 30% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 2.81.
 7. The method of claim 1 wherein the row includes no more than 20 and no less than 15 of the fan blades.
 8. The method of claim 7 wherein the chord of the fan blades at the tips is selected such that ratio of the solidity of the tips to the relative Mach number at 90% of the distance from the axial centerline to the tips is no greater than about 0.87.
 9. The method of claim 7, further comprising: establishing a predetermined relative Mach number at 60% of the radial distance from the axial centerline to the tip; selecting a chord of the fan blades at 60% of the radial distance from the axial centerline to the tip, given the predetermined relative Mach number, such that a ratio of the solidity measured at 60% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 1.50.
 10. The method of claim 9 wherein a ratio of the solidity measured at 60% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 1.35.
 11. The method of claim 10, further comprising: establishing a predetermined relative Mach number at 30% of the radial distance from the axial centerline to the tip; selecting a chord of the fan blades at 30% of the radial distance from the axial centerline to the tip, given the predetermined relative Mach number, such that a ratio of the solidity measured at 30% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 3.20.
 12. The method of claim 11 wherein a ratio of the solidity measured at 30% of the radial distance from the axial centerline to the tip, to the relative Mach number at the same radial location, is no greater than about 2.81. 